capm reading material

A STUDY ON CAPM & REALISM OF

ITS UNDERLYING ASSUMPTIONS

Adapted from Students Assignment 2011.

Table of Contents

Chapter Particulars Page No.

1 Research Design 4

2 CAPM : An Introduction 5

(i) Assumptions underlying CAPM

(ii) CAPM tools to make investment decisions - Security Market

Line, Efficiency Frontier & Capital Market Line

6

7

3 CAPM Assumptions ; A realistic Approach 9

4Comparison of Expected Returns using CAPM and Actual Returns,

based on Historic Data - and construction of SML for the same11

5 Consideration of taxes in CAPM

6Effect of inclusion of taxes on the SML and comparing with Actual

Returns using graphs21

7 Findings & Interpretations 27

8 Bibliography 28

Research Design

a) Statement of Purpose:

The basic assumption behind the CAPM model are Zero taxes and transaction costs, Homogenity,

Riskfree borrowing and lending. Since these assumptions are unrealistic, we propose to examine how

inclusion of taxes in the model will effect the Security Market Line - a decision making tool.

b) Research objectives:

Adapted from students assignment 2011.

o To understand the CAPM and related tools(SML/CML).

o Realistic examination of it’s assumption’s.

o Effect of relaxation of the assumptions on the SML and the change in the nature of the curve.

c) Research methodology:

We performed primary as well as secondary research to better understand CAPM and its usefulness in

predicting future security returns. We obtained the opinions of stock market traders on the value of CAPM

in securities analysis, who guided us in our research. We also extensively studied material available on

the internet. This project is a result of all we have understood of the subject from both these sources.

d) Research Scope:

This research gives an overview of the meaning, techniques and usefulness of CAPM. However, in depth

study of possibility of a substitute new model has not been done. Just a few examples have been taken

to understand how it works. More important is if it actually is an effective forecast for prices.

e) Research limitations

Statistical figures may not be accurate as they are estimated and not released by official sources

We've tried to be as extensive in our research as is possible, but, considering that the topic is

controversial, there may be information on the topic that is not available in the public domain.

CAPM : An Introduction

The capital asset pricing model (CAPM) is the standard risk-return model used by most academicians

and practitioners. The underlying concept of CAPM is that investors are rewarded for only that portion of

risk which is not diversifiable. This non-diversifiable risk is termed as beta, to which expected returns are

linked. The objective of the study is to test the validity of this theory in Indian capital market & the stability

of this non diversifiable risk (i.e. systematic risk or beta).

CAPM describes the relationship between risk and expected return and that is used in the pricing of risky

securities. It is based on two parameter portfolio analysis developed by Markowitz (1952). It is the

standard risk return model used by most academicians & practitioners. The underlying concept of CAPM


is that, investors are rewarded for only that portion of risk which is not diversifiable. This non-diversifiable

variance is termed as beta, to which expected returns are linked.

The general idea behind CAPM is that investors need to be compensated in two ways: time value of

money and risk. The time value of money is represented by the risk-free (rf) rate in the formula and

compensates the investors for placing money in any investment over a period of time. The other half of

the formula represents risk and calculates the amount of compensation the investor needs for taking

on additional risk. This is calculated by taking a risk measure (beta) that compares the returns of the

asset to the market over a period of time and to the market premium (Rm-rf).

Assumptions

The set of assumptions employed to develop CAPM can be summarized as follows:

I. Investors are risk averse & they have a preference for expected return & dislike of risk.

II. Investors make investment decision based on expected rate of return & the variance of the

underlying asset return. i.e. assumptions of two-parameter.

III. Investors desire to hold a portfolio that lies along the efficient frontier. (The efficient frontier is also

known as diversification frontier)


IV. There is a risk less asset & investors can lend or borrow at that risk free rate.

V. All the investments are perfectly divisible. That is, the fractional shares for any investment can be

purchased in any moment.

VI. All the investors have the homogeneous expectations regarding investment horizon or holding

period and to forecasted expected return & level of risk on securities. At the same time, there is a

complete agreement among investors as to the return distribution for each security & portfolio.

VII. There are no imperfections in the market that prevent the investors to buying or selling the assets.

More importantly, there are no commissions or taxes involved with the security transaction. That

means, there are no costs involved in diversification & there is no differential tax treatment of

capital gain & ordinary income.

VIII. There is no uncertainty about expected inflation, or alternatively, all security prices are fully reflect

all changes in future inflation expectations.

IX. Capital market is in equilibrium. That is all the investment decisions have been made & there is no

further trading without new information.

CAPM tools to make investment decisions

SECURITY MARKET LINE (SML)

The SML will tell us assets’ required returns, given their level of systematic risk (as measured by

beta).We can compare this to the assets’ expected returns (given our forecasts of future prices and

dividends) to identify undervalued assets and create the appropriate trading strategy.

An asset with an expected return greater than its required return from the SML is undervalued; we

should buy it.

An asset with an expected return less than the required return from the SML is overvalued; we

should sell it (or short sell it if we’re inclined to be aggressive).

An asset with an expected return equal to its required return from the SML is properly valued;

we’re indifferent between buying and selling it.


Example : The following table contains information based on analyst’s forecasts for three stocks. The risk-free

rate is 7 percent and the expected market return is 15 percent. Compute the expected and required return on

each stock, determine whether each stock is undervalued, overvalued, or properly valued, and outline an

appropriate trading strategy.

Stock Price today E(Price) in 1 year E(Divid.) in 1 year Beta

Stock A 25 27 1.00 1.0

Stock B 40 45 2.00 0.8

Stock C 15 17 0.49 1.2

Answer: Expected and required returns are shown in the figure below:

Expected Return Required Return

A (27 -25 +1) / 25 = 12.0% 0.07 + (1.0) (0.15 – 0.07) = 15.0%

B (45 - 40 + 2) / 40 = 17.5% 0.07 + (0.8) (0.15 – 0.07) = 13.4%

C (17 - 15 + 0.49) / 15 =

16.6%

0.07 + (1.2) (0.15 – 0.07) = 16.6%

A is overvalued. It’s expected to earn 12%, but based on its systematic risk it should earn 15%.

B is undervalued. It’s expected to earn 17.5%, but based on systematic risk it should earn 13.4%.

C is properly valued. It is expected to earn 16.6%, & based on systematic risk it should earn 16.6%.

The appropriate trading strategy is: Short sell A, buy B and buy, sell, or ignore C.

EFFICIENCY FRONTIER & CAPITAL MARKET LINE

The efficient frontier consists of the set portfolios that has the maximum expected return for a given risk

level.


SML for stock C

Rf = 7%

R(k) = 16.6%

Beta 1.0

Rm=15%

SML

1.2

R(k) = 7% + 1.2[8%] = 16.6%

E(k)

Rf = 7%

R(k) = 16.6%

Beta 1.0

Rm=15%

SML

1.2

R(k) = 7% + 1.2[8%] = 16.6%

E(k)

B

D

C

30

40

50

60

70

80

B D

standard deviation

exp

ecte

d r

etu

rn

Efficiency frontier

C

For every level of standard deviation along the X axis, the efficient frontier records the portfolio with the

highest expected return (e.g. B & D). No investor would choose Portfolio C because portfolio B has a

higher expected return for the same level of risk. Asset allocation along the efficiency frontier changes to

provide diff risk-return combos. D will correspond to & 70% equity & B 30 % equity. Higher return - higher

risk.

Capital Market Line (CML): is the line of tangency between the RFR point on the vertical axis and the

efficient frontier.

The CML is considered to be superior to the efficient frontier since it takes into account the inclusion of a

risk-free asset in the portfolio. The portfolio at the point of tangency is the market portfolio. Market

portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the

proportions that they exist in the market. The MP is the only risky portfolio anyone would hold and is the

only source of risk. As per risk tolerance, all investors choose a combo of risk free asset and market

portfolio. The capital asset pricing model (CAPM) demonstrates that the market portfolio is essentially the

efficient frontier. This is achieved visually through the security market line (SML).

CAPM Assumptions - A Realistic Approach (Relaxation)Adapted from students assignment 2011.

M

0

10

20

30

40

50

60

70

80

M

standard deviation

exp

ecte

d r

etu

rn

Efficiencyfrontier

Rf

Capital market Line

With the data presented thus far regarding efficiency of capital markets, the assumptions of the CAPM

can be relaxed on these grounds :

The model assumes that the variance of returns is an adequate measurement of risk. This might be

justified under the assumption of normally distributed returns, but for general return distributions other

risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately.

Indeed risk in financial investments is not variance in itself, rather it is the probability of losing: it is

asymmetric in nature

1. Differential borrowing and lending rates: There is only one risk free rate in the model. This is an

unrealistic assumption. Investors cannot borrow and lend at the same rate. Two rates mean 2

CMLs (as shown in the graph below). One implication of differential borrowing and lending rates is

that the borrowing portfolio is not as profitable as when it assumed investors could borrow at risk

free rate.

2. Heterogeneous expectations : If all investors have different expectations about risk and return,

each would have a unique CML and/or SML, and the composite graph would be a band of lines

with a breadth determined by the divergence of expectations. The CAPM assumes invests have

the same beliefs about expected returns and risks of available investments. But we know that

there is massive trading of stocks and bonds by investors with different expectations.

3. Differing planning periods : if one investor uses a one-year planning period and another uses a

one-month planning period, then the two investors have different SML.


E(R)

Rb

RFR

Risk (standard deviation )

F

G

K

E(R)

Rb

RFR

Risk (standard deviation )

F

G

K

4. Taxes Exist : Zero taxes. The CAPM assumes investment trading is tax-free and returns are

unaffected by taxes. Yet we know this to be false: (1) many investment transactions are subject to

capital gains taxes, thus adding transaction costs; (2) taxes reduce expected returns for many

investors, thus affecting their pricing of investments; (3) different returns (dividends versus capital

gains, taxable versus tax-deferred) are taxed differently, thus inducing investors to choose

portfolios with tax-favored assets; (4) different investors (individuals versus pension plans) are

taxed differently, thus leading to different pricing of the same assets.

5. Transaction costs Exist: The cost trading the security may offset any potential excess return

resulting from the trade securities will plot close to SML but not exactly on it (shown below).

Transaction costs also limit diversification, because at some point , the additional cost of

diversification would exceed its benefits

6. Non availability of risk free assets : The CAPM assumes the existence of zero-risk securities, of

various maturities and sufficient quantities to allow for portfolio risk adjustments. But we know

even Treasury bills have various risks.

Comparison of SML & Actual Returns Based on Historic Data

In order to understand the deviation between the returns calculated using CAPM and the actual

returns, the following steps have been taken:


E(R)

E(Rm)

i

SML

0.0 1.0

E(Rz)

E(RFR) or

1. Five Stocks have been selected from the Nifty 50 for purpose of analysis

2. Construction of SML:

a) The variables in the CAPM model were collected as follows :

i) Risk Free Rate of Return - This has been obtained using the 10 year Indian

government bond yield for the respective periods.

ii) Beta - Obtained from the NSE website for the respective periods from archives

iii) Estimated Market Rate of Return - This data has been collected from .

b) SML was constructed in the manner described in the previous pages for each period.

3. Actual Returns are computed on the basis of historic prices (obtained from NSE) using the

formula:

AR = P1 - P0

P0

For example if Actual Returns for Jan 2008 are being computed:

P1 = Market Price of Stock in Jan 2008

P0 = Market Price of Stock in Jan 2007

D1 = Dividend during period Jan 2007-08

Actual returns for the periods are specified next to the respective charts.

Stock 1: Suzlon

Year Risk Free rate

Beta Expected Market Rate of Return (NIFTY)

CAPM Return R(k)

Actual Returns

Jan-08 7.72 1.05 -51.83 -54.8172 -96.806Jan-09 5.96 1.53 71.45 106.1597 36.27451Jan-10 7.63 1.5 17.24 22.045 -39.121



-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.72

Rm = -51.84

R( k ) = -54.81R(k)

Jan 2008

1.05

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.72

Rm = -51.84

R( k ) = -54.81R(k)

Jan 2008

1.05

0

10

20

30

40

50

60

70

80

90

100

110

120

0 0.5 1 1.5 2

Beta

Return

SML

Rf = 5.96

Rm = 71.45

R( k ) = 106.16

R(k)

1.53

Jan 2009

0

10

20

30

40

50

60

70

80

90

100

110

120

0 0.5 1 1.5 2

Beta

Return

SML

Rf = 5.96

Rm = 71.45

R( k ) = 106.16

R(k)

1.53

Jan 2009

0

3

6

9

12

15

18

21

24

0 0.5 1 1.5 2

Beta

Return

SML

Rf = 7.63

R(k) = 22.045

Rm = 17.24

R(k)

Jan 2010

0

3

6

9

12

15

18

21

24

0 0.5 1 1.5 2

Beta

Return

SML

Rf = 7.63

R(k) = 22.045

Rm = 17.24

R(k)

Jan 2010

Stock 2: ACC


Year Risk Free rate


CAPM Return R(k)

Actual Returns

Jan-08 7.72 0.89 -51.83 -45.28 -53.2389Jan-09 5.96 0.69 71.45 51.1481 79.32199Jan-10 7.63 0.79 17.24 15.2219 19.67071

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rm = -51.84

Rf = 7.72

R(k) = -45.28 R(k)

0.89

Jan 2008

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rm = -51.84

Rf = 7.72

R(k) = -45.28 R(k)

0.89

Jan 2008

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

Rm = 71.45

Rf = 5.96

R(k) = 51.15 R(k)

0.69

Jan 2009

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

Rm = 71.45

Rf = 5.96

R(k) = 51.15 R(k)

0.69

Jan 2009

Stock 3: Bharti Airtel

Year Risk Free rate


CAPM Return R(k)

Actual Returns

Jan-08 7.72 0.89 -51.83 -45.2877 -25.9154Jan-09 5.96 0.92 71.45 66.2108 -54.11Jan-10 7.63 0.93 17.24 16.5673 9.3230


0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

Rm = 17.24

Rf = 7.63

0.79

R(k) = 15.22R(k)

Jan 2010

0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

Rm = 17.24

Rf = 7.63

0.79

R(k) = 15.22R(k)

Jan 2010


-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.72

Rm = -51.839

R( k ) = -45.28R(k)

0.89

Jan 2008

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.72

Rm = -51.839

R( k ) = -45.28R(k)

0.89

Jan 2008

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

Rf = 5.96

Rm = 71.45

R( k ) = 66.2108 R(k)

0.92

Jan 2009

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

Rf = 5.96

Rm = 71.45

R( k ) = 66.2108 R(k)

0.92

Jan 2009

0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.63

Rm = 17.24

R( k ) = 16.56

R(k)

0.93

Jan 2010

0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.63

Rm = 17.24

R( k ) = 16.56

R(k)

0.93

Jan 2010

Stock 4: ITC

Year Risk Free rate


CAPM Return R(k)

Actual Returns

Jan-08 7.72 0.65 -51.83919271 -30.9935 -21.1519Jan-09 5.96 0.54 71.45 41.3246 46.44125Jan-10 7.63 0.61 17.24 13.4921 -30.7418


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-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.72

Rm = -51.84

R( k ) = -30.99

R(k)

0.65

Jan 2008

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.72

Rm = -51.84

R( k ) = -30.99

R(k)

0.65

Jan 2008

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

Rf = 5.96

Rm = 71.45

R( k ) = 41.32

R(k)

0.54

Jan 2009

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

Rf = 5.96

Rm = 71.45

R( k ) = 41.32

R(k)

0.54

Jan 2009

Stock 5: Tata Motors

Year Risk Free rate


CAPM Return R(k)

Actual Returns


0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.63

Rm = 17.24

R( k ) = 13.49R(k)

0.61

Jan 2010

0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.63

Rm = 17.24

R( k ) = 13.49R(k)

0.61

Jan 2010

Jan-08 7.72 0.83 -51.83 -41. 4.835493Jan-09 5.96 1.04 71.45 74.0696 378.0882Jan-10 7.63 1.23 17.24 19.4503 60.46098


-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.72

Rm = -51.84

R( k ) = -41.71 R(k)

0.83

Jan 2008

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.72

Rm = -51.84

R( k ) = -41.71 R(k)

0.83

Jan 2008

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

Rf = 5.96

Rm = 71.45

R( k ) = 74.07

R(k)

1.04

Jan 2009

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

Rf = 5.96

Rm = 71.45

R( k ) = 74.07

R(k)

1.04

Jan 2009

0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.63

Rm = 17.24

R( k ) = 19.45

R(k)

1.23

Jan 2010

0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

Rf = 7.63

Rm = 17.24

R( k ) = 19.45

R(k)

1.23

Jan 2010

INTERPRETATION

As is seen in the charts and table above, there is a vast difference between the Expected returns

calculated using the Capital Asset Pricing Model (CAPM) and the Actual Returns computed as per

historic prices.

One must keep in mind that in the 3 year period selected above - there was a global recession,

following which the Stock Market Indices also took unpredictable paths.

When one uses the CAPM, the Rm is calculated on the basis of historic Indices data and is only an

estimate - and this variable can drastically change the expected returns as per CAPM. This is

because the Beta, being a risk measure, is also calculated using historic Indices data. Thus, the

recession can be considered as one of the reasons for variations.

However, even allowing a margin for the unusual external factors mentioned above, the disparity is

high enough to show that CAPM assumptions are unrealistic and its value as a practical tool must be

questioned. Thus, we proceed to examine how considering taxes in the CAPM formula may impact

the returns.

Considering Taxes & Transaction Costs In CAPM

On including tax in the CAPM formula as follows : Re = Rf (1-t) + B [Rm (1-t)- Rf(1-t)],

The following marginal changes in return are observed:


Year Risk Free rate (Rf)

Beta Expected Market Rate of Return (NIFTY) (Rm)

Tax rate

CAPM Return R(k)

CAPM return with taxes (Re)

Actual Returns (AR)

Difference

SUZLON

Jan-08 7.72 1.05 -51.83 33.99% -54.8172 -36.1848 -96.806 60.6212Jan-09 5.96 1.53 71.45 33.99% 106.1597 70.07602 36.27451 33.80151Jan-10 7.63 1.5 17.24 33.99% 22.045 14.5519 -39.121 53.6729

BHARTI AIRTEL

Jan-08 7.72 0.89 -51.83 33.99% -45.2877 -29.8944 -25.9154 -3.97903Jan-09 5.96 0.92 71.45 33.99% 66.2108 43.70575 -54.11 97.81576Jan-10 7.63 0.93 17.24 33.99% 16.5673 10.93607 9.323097 1.612978

TATA MOTORS

Jan-08 7.72 0.83 -51.83 33.99% -41.7141 -27.5355 4.835493 -32.371Jan-09 5.96 1.04 71.45 33.99% 74.0696 48.89334 378.0882 -329.195Jan-10 7.63 1.23 17.24 33.99% 19.4503 12.83914 60.46098 -47.6218

ITC

Jan-08 7.72 0.65 -51.83 33.99% -30.9935 -20.4588 -21.1519 0.693112Jan-09 5.96 0.54 71.45 33.99% 41.3246 27.27837 46.44125 -19.1629Jan-10 7.63 0.61 17.24 33.99% 13.4921 8.906135 -30.7418 39.64793

ACC

Jan-08 7.72 0.89 -51.83 33.99% -45.2877 -29.8944 -53.2389 23.34455Jan-09 5.96 0.69 71.45 33.99% 51.1481 33.76286 79.32199 -45.5591Jan-10 7.63 0.79 17.24 33.99% 15.2219 10.04798 19.67071 -9.62273

Thus, we observe that the inclusion of taxes in the formula in the formula makes a marginal

difference.

Effect of Inclusion of Taxes on SML & Comparison With Actual

Returns

NOTE : R(k) referred to in these charts is the expected returns calculated as per CAPM on inclusion

of taxes.


Stock 1 : Suzlon


-110

-100

-90

-80

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-60

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-40

-30

-20

-10

0

10

20

0 0.5 1 1.5Beta

Return

SML

AR

Rf = 7.72

Rm = -51.84

R( k ) = -36.1848

Jan 2008

1.05

AR = -96.806

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5Beta

Return

SML

AR

Rf = 7.72

Rm = -51.84

R( k ) = -36.1848

Jan 2008

1.05

AR = -96.806

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2

Beta

Return

SML

AR

Rf = 5.96

Rm = 71.45

AR = 36.27451

R(k)= 70.07

1.53

Jan 2009

-42-39-36-33-30-27-24-21-18-15-12

-9-6-30369

12151821

0 0.5 1 1.5 2

Beta

Return

SML

AR

Rf = 7.63

AR = -39.121

Rm = 17.24R(k) =14.5

Jan 2010

-42-39-36-33-30-27-24-21-18-15-12

-9-6-30369

12151821

0 0.5 1 1.5 2

Beta

Return

SML

AR

Rf = 7.63

AR = -39.121

Rm = 17.24R(k) =14.5

Jan 2010

Stock 2: Bharti Airtel


-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

AR

Rf = 7.72

Rm = -51.839

AR = --25.9154

-29.8944

0.89

Jan 2008

-70-60

-50-40-30-20

-100

1020

30405060

7080

0 0.5 1 1.5

Beta

Return

SML

ARRf = 5.96

Rm = 71.45

AR = -54.11

R(k)= 43.70

0.92

Jan 2009

Stock 3: Tata Motors


0

3

6

9

12

15

18

21

0 0.5 1 1.5

Beta

Return

SML

AR

Rf = 7.63

Rm = 17.24

AR = 9.32

R(k) = 10.93

0.93

Jan 2010

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

AR

Rf = 7.72

Rm = -51.84

AR= 4.83

R(k)=-27.5355

0.83

Jan 2008

Stock 4 : ITC


0

50

100

150

200

250

300

350

400

0 0.5 1 1.5

Beta

Return

SML

AR

Rf = 5.96

Rm = 71.45

AR = 378.08

R(k)= 48.89

1.04

Jan 2009

0

10

20

30

40

50

60

70

0 0.5 1 1.5

Beta

Return

SML

AR

Rf = 7.63

Rm = 17.24

R( k ) = 19.45

AR=60.46

1.23

Jan 2010

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

AR

Rf = 7.72

Rm = -51.84

AR = -21.1519 R(k)= -20.4588

0.65

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

AR

Jan 2008

Stock 5 : ACC


0

10

20

30

40

50

60

70

80

0 0.5 1 1.5

Beta

Return

SML

AR

Rf = 5.96

Rm = 71.45

AR= 46.44

R(k)=27.27

0.54

Jan 2009

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

AR

Rf = 7.63

Rm = 17.24

AR = -30.74

R(k)= 8.90

0.61

Jan 2010

-60

-50

-40

-30

-20

-10

0

10

20

0 0.5 1 1.5

Beta

Return

SML

AR

Rm = -51.84

Rf = 7.72

R(k)= -29.8944

0.89

AR = -53.23

Jan 2008

FINDINGS & INTERPRETATIONS


0

10

20

30

40

50

60

70

80

90

0 0.5 1 1.5

Beta

Return

SML

AR

Rm = 71.45

Rf = 5.96

R(k) = 33.76286

0.69

AR = 79.32199

Jan 2009

0

10

20

30

0 0.5 1 1.5

Beta

Return

SML

ARRm = 17.24

Rf = 7.63

0.79

R(k)= 10.04798

AR = 19.67071

Jan 2010

On the premises of data collected, analysed and observed, the Capital Asset Pricing Model proves to

be one that can only generate a trendline i.e. the behaviour of returns at differing degrees of

systematic risk. Capital Asset Pricing Model proves to be ineffective with or without taxes.

The behaviour of the SML which we set out to study, changes drastically on inclusion of taxes in the

model. There is no longer a linear relationship between market return and expected returns as per

CAPM. Rather the nature of the curve itself changes to a non - linear curve showing the non -

correlation of market returns to forecasted returns on inclusion of taxes.

However, even on inclusion of the taxes in the model, the model was ineffective in forecasting the

actual returns for the future periods.

Many reasons can be attributed to the inadequacy of the model. The uncertainty in market

conditions, and hence, difficulty in predicting the expected market return on historic index trends

leads to variation between expected and actual returns. Furthermore, even Beta is computed on the

basis of past historic data, and there is no reliability that if the market moves a certain percentage

points upwards, the stock will also move as a multiple of that movement.

Thus, on closer observation, we see that the assumptions of CAPM are not its only weakness, as was

assumed at the beginning of the Research project.

As a recommendation, we suggest that even if reasonably sound estimate of Market Return can be

made, a study in finding an alternative to use of Beta as the measure of risk and measure of

correlation to the market be made. A detailed analysis of an alternative to correlate the market and

stock be made.

BIBLIOGRAPHYAdapted from students assignment 2011.

www.nseindia.com : to obtain historic indices, stock prices

www.tradingeconomics.com : to obtain 10 year Indian government bond yield

www.wikipedia.com : to obtain theoretical understanding of CAPM


http://www.wikipedia.com/

http://www.tradingeconomics.com/

http://www.nseindia.com/

capm reading material

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